SOLUTION: find the length of the short leg of a right triangle if the longer leg is 11 feet more than the shorter leg and the hypotenuse is 11 feet less than twice the shorter leg
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Question 655170: find the length of the short leg of a right triangle if the longer leg is 11 feet more than the shorter leg and the hypotenuse is 11 feet less than twice the shorter leg Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! find the length of the short leg of a right triangle if the longer leg is 11 feet more than the shorter leg and the hypotenuse is 11 feet less than twice the shorter leg
.
Let x = length of shorter leg
then
x+11 = longer leg
2x-11 = hypotenuse
.
Applying Pythagorean's theorem:
x^2 + (x+11)^2 = (2x-11)^2
x^2 + (x+11)(x+11) = (2x-11)(2x-11)
x^2 + (x^2+22x+121) = 4x^2-44x+121
2x^2+22x+121 = 4x^2-44x+121
22x+121 = 2x^2-44x+121
121 = 2x^2-66x+121
0 = 2x^2-66x
0 = 2x(x-33)
x = {0, 33}
throw out the zero (extraneous) leaving
x = 33 feet
